Local environmental dependence on weak-lensing shear statistics

Despite the assumption that an ideal FLRW observer is not dependent on the local environment, observations are biased by the positions of the observers due to the matter correlations in the large-scale structure (LSS) of the universe. The variation of the mass distribution of the LSS of the universe implies that observers residing in different locations may suffer bias in their measurements when they look at the images of distant galaxies. Here, we assess the influence of the local environment on weak gravitational lensing (WL) shear statistics in the context of relativistic $N$-body code, \texttt{gevolution}. We derive numerical constraints on the cosmological parameters from the WL shear angular power spectrum and comment on the local environment's influence on WL shear. We find tighter constraints on the parameter $\Omega_\mathrm{m}$ above redshift $z$ = 0.2, which implies over this redshift the local environment's impact is minor. We also investigate the bispectrum and conclude that on average the impact of the local environment on $f_{\rm NL}$ (a measure of non-Gaussianities) is minimal and consistent with zero effect. However, we find that within the assembly of all possible observers/locations, there will also be a few that could infer the parameter $f_{\rm NL}$ of the order 10. These results could thus be used to estimate the uncertainty in the inference of cosmological parameters such as $f_{\rm NL}$ based on WL shear bispectrum and thus may have implications for future surveys requiring precision at the percent level.